Changing the shape of the wall from a circle to something longer and thinner isn't easy in Illustrator (might be easier in PS). One way is to simply expand the effect, then scale the thing so it's thinner. If you're doing this, make a note of the numeric scaling value, then create a variant of your wallpaper fattened by 1 over that value as a decimal so you end up with non-distorted wallpaper (e.g. if you're going to make it 80% width, 1 / 0.8 = 1.25 so stretch the wallpaper 125% width).

Here's a low-res example with 800% / 12.5% scaling:

No infinity, but up the perspective and increase the scaling until the end point gets close to being less than 1px or one dot on a printed page, then just let it disappear.

I would just use the perspective plane in the Vanishing Point filter to get the first perspective right. I would then convert it to a smart object to preserve the quality. I think after that you might be able to use the Warp tool and curve the top of the image (top left & top right) to match that perspective curve in your example.

I haven't tried this — so I could be mistaken. . Just as a heads up.... :)

It reminds me of my own interest in mapping 2D images from Illustrator into PS in order to mock up a design on a mug or other curved surface. The options in the Vanishing Point filter seem a little janky for something so (seemingly) simple.